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(D) The given line is $5x + 2y + 7 = 0$. Its slope is $m_1 = -\frac{5}{2}$. Any line perpendicular to this line will have a slope $m_2 = -\frac{1}{m_1

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$5dy - 2dx = 0$

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(D) The given line is $5x + 2y + 7 = 0$. Its slope is $m_1 = -\frac{5}{2}$. Any line perpendicular to this line will have a slope $m_2 = -\frac{1}{m_1} = \frac{2}{5}$. The equation of a family of lines with slope $\frac{2}{5}$ is $y = \frac{2}{5}x + c$,which can be written as $2x - 5y + 5c = 0$. Let $5c = k$,so the equation is $2x - 5y + k = 0$. Differentiating both sides with respect to $x$,we get $2 - 5\frac{dy}{dx} = 0$. Multiplying by $dx$,we get $2dx - 5dy = 0$,or $5dy - 2dx = 0$.

The differential equation of all lines perpendicular to the line $5x + 2y + 7 = 0$ is

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